Cons
More setup involved than with a hardside trailer.
Setting up in the rain.
Packing usually takes longer because of storage.
Storage.
Less space to move around.
More outside noise coming in (annoying neighbors, cars, dogs barking, etc)
More inside noise going out.
Longer breakdown of camp.
Can be harder to cool in really hot areas.
Pros
Easier to tow.
Easier to store in most cases.
Better fuel mileage.
Doesn't require as big of tow vehicle in many cases.
More outside noises coming in (good noises like birds singing and waves).
Fits in more sites.
Can get the same amenities as a hardside trailer.
Possible to get to more remote sites.
Fewer tires to replace (Most Pups are single axle).
Generally don't need weight distribution hitches.
I'm sure there are plenty more, but it is early for me.